1. Generally speaking, if every term of a polynomial has a common factor, you can put this common factor in parentheses and write the polynomial in the form of factor product. This method of decomposing factors is called the improved common factor method.
2. Grouping decomposition refers to the decomposition of factors that cannot be directly decomposed by common factor method and formula decomposition method. Decomposition methods are generally divided into "1+3" and "2+2".
3. The undetermined coefficient method is an important method in junior middle school mathematics. The factorization of undetermined coefficient method refers to the assumption that the original formula is the product of several factors according to known conditions. The coefficients in these factors can be expressed by letters first, and their values are undetermined. Because the continuous product of these factors is the same as the original formula, the equations of undetermined coefficients are established according to the principle of identity, and the values of undetermined coefficients can be obtained by solving the equations.
4. Simply put, the method of cross decomposition is: the multiplication on the left side of the cross is equal to the quadratic term coefficient, the multiplication on the right side is equal to the constant term, and the multiplication and addition of the cross are equal to the linear term coefficient. In fact, it is to use the multiplication formula (x+a)(x+b)=x? +(a+b)x+ab for factorization.
5. Double cross multiplication is a factorization method. For Ax and other types? +Bxy+Cy？ The polynomial factorization of +Dx+Ey+F usually uses the undetermined coefficient method. The operation process of this method is complicated. For this problem, if the "double cross multiplication" (principal component method) is adopted, this kind of polynomial can be easily factorized.
6. If the result is the same as the original formula, the multivariate polynomial is said to be a symmetric polynomial about any two elements. x？ +y？ +z？ , xy+yz+zx are all symmetric polynomials about the elements x, y and z.